The name is absent

Chapter 2

aggregation. This process is usually referred to as slow aggregation.

For fast aggregation, if it is Brownian diffusion dominated, the process is
referred to as perikinetic aggregation and the rate of change of the number of
droplets per unit volume N is given by^[18]:

- ʃ = k_pN² = (8^)7V² = (⅛², W) = --~⅞-          [2.13]

dt                       3η              1 + k_pN_tJ

Here D is the diffusion coefficient of the droplets, η is the viscosity of the
continuous phase and N₀ is the initial number concentration Ofdroplets in solution.

If non-Brownian forces dominant the displacement of the droplets,
aggregation is termed as Orthokinetic^[18]. In this case, the rate is:

-^ = 4„№=(|л’С)№, N(I) = ʌ''¹                        [2.14]

at            3                  1 + k₀N₀t

Here G is the velocity gradient, ко is the Orthokinetic rate constant. At room
temperature, perikinetic aggregation would be more significant for smaller
particles (R < 2 μm) and Orthokinetic aggregation would dominate otherwise (R >
5 μm).

For slow aggregation, the rate is ^[19]:

_dN_₌k^_Ni                             [2.15]

dt W

Here k_p is the perikinetic rate and И/is the so-called stability ratio.

19

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